Observational results:

Core models:

Expanded models:

Only the Guidance coeficients

Experiment Results (dummy)

Core models:

Expanded models:

Interaction

In order to add errors to marginal effects, I need the covariance.

It might be good to show the underlying data, which would look better (and be more accurate) for the 5pt scale, but could be jittered on 1 and 0.

## # A tibble: 4 x 3
##   group               condition         estimate
##   <chr>               <chr>                <dbl>
## 1 Lobbied on Guidance Guidance Vignette    0.177
## 2 Lobbied on Rule     Rule Vignette        0    
## 3 Lobbied on Rule     Guidance Vignette   -0.612
## 4 Lobbied on Guidance Rule Vignette       -0.827

The effect of the guidance condition for those that lobbied on guidance compared to:

The rule condition for those that lobbied on guidance: 1.003293

The guidance condition for those that lobbied on a rule: 0.78819

The rule condition for those that lobbied on a rule: 0.176623

Experiment Results (5 point)

Core models:

Interaction

## # A tibble: 4 x 3
##   group               condition         estimate
##   <chr>               <chr>                <dbl>
## 1 Lobbied on Guidance Guidance Vignette   0.0155
## 2 Lobbied on Rule     Rule Vignette       0     
## 3 Lobbied on Rule     Guidance Vignette  -0.494 
## 4 Lobbied on Guidance Rule Vignette      -0.657

The effect of the guidance condition for those that lobbied on guidance compared to:

The rule condition for those that lobbied on guidance: 0.6721448

The guidance condition for those that lobbied on a rule: 0.5092595

The rule condition for those that lobbied on a rule: 0.0155363

For refrence: For 𝑌=𝑏0+𝑏1𝑋+𝑏2𝑍+𝑏3𝑋𝑍+𝑒 , the marginal effect is 𝑏1+𝑏3⋅𝑍, a function of 𝑍. The variance of a weighted sum is 𝑉𝑎𝑟(𝑏1)+𝑉𝑎𝑟(𝑏3)⋅𝑍2+2⋅𝑍⋅𝐶𝑜𝑣(𝑏1,𝑏3), and the standard error is just the square root of that. You can get the covariance from the right off-diagonal element of the variance-covariance matrix of the coefficients. The variances will be found on the diagonal.

Citations

Anthony (1992)

F. R. Baumgartner (2009)

F. R. Baumgartner and Jones (1993)

F. R. Baumgartner and Leech (2001)

Bentham (1843)

Browne (1990)

D. P. Carpenter (2002)

D. P. Carpenter and Moss (2014)

Coglianese, Kilmartin, and Mendelson (2009)

Davis (1971)

Dür and De Bièvre (2007)

Epstein and O’Halloran (1995)

Food and Drug Administration (2011)

Franklin (2010)

Funk (2001)

Scott R. Furlong (1998)

Scott. R. Furlong and Kerwin (2005)

Garrett and Vermeule (2006)

Gluck, Po, and Joseph O’connell (2015)

Golden (1998)

Graham and Broughel (2015)

Greve and Parrish (2014)

Haeder and Yackee (2015)

Hojnacki et al. (2012)

Hickman (2009)

Hrebenar and Scott (1996)

Hwang et al. (2014)

Kaufman (1981)

Kaufman (2001)

Kerwin and Furlong (2018)

Kingdon (1995)

Klüver (2013)

Levin (2018)

Lewis (2011)

Magill (2004)

Mahoney (2007)

Manning (1996)

Mantel (2009)

McCubbins, Noll, and Weingast (1987)

McCubbins, Noll, and Weingast (1987)

N. Mendelson (2007)

Naughton et al. (2009)

Office of Management and Budget (2007)

Parrillo (2019)

Romano (2014)

Romano (2018)

Raso (2010)

Rourke (1984)

Rosenbloom (2000)

Sabatier (1988)

Schattschneider (1975)

Seidenfeld (2011)

Shapiro (2014)

Stack (2016)

Truman (1951)

Warren (2011)

West (1995)

West (2004)

Yackee (2019)

J. W. Yackee and Yackee (2006)

Young, Marple, and Heilman (2017)

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